The PI studies a variety of problems in non-holonomic dynamics. The study is related with rigidity theory, the theory of completely integrable systems with continuous and discrete time, contact geometry, and the theory of Hill's equation. The main theme of the research is an interaction between continuous and discrete, and between rigidity and flexibility. The methods of study are mostly geometrical. The project has grown out of the PI's work in these areas in the last several years.
This research project has a potential of making an impact in a number of applied fields including vehicle motion theory, pursuit problems, theoretical robotics, and flotation theory. The developed methods and new insights will find applications in various other problems of contemporary interest, modeled by ordinary differential and finite difference equations. The PI is the Director of the Mathematics Advance Studies Semesters Program (MASS) at Penn State. The project has an additional impact by engaging the MASS participants, advanced undergraduate students from across the USA, and influencing their career choices in mathematics and related disciplines.